[其他] Has Barro solved the equity premium puzzle? [推广有奖]

国外blogs的一篇文章，作者未知，此blogs给屏蔽了，所以转过来，供研究equity premium puzzle 者参考。

It's not quite the holy grail of financial economics, but certainly one of the longest running debates has been over what is known as the equity premium puzzle - or why US stock returns are so much higher than returns on Treasury bonds. The seminal paper was by Rajnish Mehra and Edward C.Prescott in 1985: "The Equity Premium: A Puzzle" published in the Journal of Monetary Economics. Mehra and Prescott showed it was difficult to reconcile empirical facts about equity and debt returns with reasonable assumptions about the relative rate of risk aversion and the pure rate of time preference, posing difficulties for the capital asset pricing model.

A new paper by Robert Barro to this year's Minnesota Workshop in Macroeconomic Theory attempts to answer the puzzle: Rare Events and the Equity Premium .Barro's paper builds upon a 1988 JME article by Thomas Rietz entitled "The equity premium: A solution" , which argued that the premium could be explained by infrequent but very large falls in consumption (i.e. wars, depressions or disasters), if the intertemporal elasticity of substitution of consumption is low. Or as Brad DeLong recently put it:

Rietz's (1988) answer to the equity premium puzzle was this: a long, fat lower tail to the return distribution. A small probability of very bad things happening to stock returns could support both (a) a relatively small sample variance of returns, and (b) rational aversion to large-scale stock ownership large enough to produce the observed equity premium. The question that Rietz was unable to answer was: "What exactly are these very bad things?"

Mehra & Prescott immediately dismissed the Rietz arguments in a 1988 JME article ,concluding:

Are Rietz's disaster scenarios reasonable? They are undoubtedly extreme. That such extreme assumptions are needed to account for the average returns on debt and equity we interpret as supporting our contention that standard theory still faces an unsolved puzzle.

But Barro has resurrected Rietz, and added his own twist. Barro explained the origins of his 2005 paper in an interview just published by the Minneapolis' Fed's journal, The Region:

Mehra and Prescott were extremely critical of the Rietz analysis, and I think they managed to convince most people that low-probability disasters were not the key to the equity premium puzzle. But, although I highly value the insights in their original 1985 paper (which Mehra and Prescott like to point out was actually written in 1979), I think the arguments in their 1988 comment on Rietz were incorrect.

I had not thought much about this issue until a few months back—it's not an area that I've worked in. But when I began to study it, it seemed that low-probability disasters could be quite important. And then I found Rietz's paper, which I thought was a great insight, and I have been building on it. Frankly, I think this idea explains a lot. Of course, there is a good deal more to work out, to think about further, but I think his basic insight is correct.

He elaborates:

Suppose that you have potential events with, say, a 1 percent annual probability, where you lose half of your capital stock and GDP. This possibility seems to be enough to get something like the observed equity premium. Moreover, this mechanism has implications for a lot of other variables, not just for the excess of the average return on stocks over the return on government bills. For example, it can explain the very low “risk-free” rate and low expected real interest rates during most U.S. wars back to the Civil War. It can also explain some of the evolution of price-earnings ratios for the U.S. stock market.

...I've looked at the 20th century history of large, short-term economic contractions as a way of motivating the general orders of magnitude for the parameters in the model. So, looking at the world wars and the Great Depression, and other depressions—for example, in Latin America and Asia in the post-World War II period—you find a substantial number of these events. If you take that whole history covering many countries over 100 years, you get some idea of the probability and potential size of these rare disasters. I show in the model that if you use these “reasonable” parameters, the theoretical results match up with empirical observations, such as the equity premium.

Brad DeLong disagrees with this line of reasoning, arguing that in order for Rietz to be correct:

Any macroeconomic factor to drive the equity premium must therefore be a factor that leaves the real value and real return on short-period U.S. Treasury securities unaffected. But almost all true macroeconomic disasters that could halve or do worse to the real value of equities are likely to produce at the very least rapid and substantial inflation, if not confiscatory taxes on or outright repudiation of government bonds.

An economic depression would be deflationary, surely? As for war, while one can see how tight capacity constraints would be inflationary, Barro argues in The Region interview that real bond yields were actually low during wartime:

...I argue that this approach can explain a lot of the real-interest-rate movements in the U.S. history—particularly why expected real interest rates were very low during the main wartime periods in the United States, including the Civil War, World War I, World War II and the Korean War.

This is a fascinating debate that will likely not conclude anytime soon. For example, Cyber Libris blog recently raised two issues about the Rietz/Barro argument that merit consideration:

Two intertwined things worry me though. First, the Rietz/Barro argument sounds like the quantum leap debate in physics (disclosure: My field is not physics!). A lot of the literature in the economics of risk and uncertainty has provided evidence that people usually underestimate low probability events (from Howard Kunreuther to Nassim Taleb's famous Black Swan, ). People have a hard time moving from the "normal" to the "rare" and back. How come that things (chief among them behaviors) are not the same in the small and in the large? So, who's right? Those who believe in the Black Swan or those who don't? More work is needed and it does not relate to finance only (think of climate events etc...).

Second, University of California Philippe Jorion and Yale University William N Goetzmann have shown that when you gather more data from more markets (outside the US) you get an empirical premium that is lower than the one that has been estimated on the US market only. Question: How do you reconcile the two sets of observations and arguments? In other words, is the premium too low or too high, is it vanishing and what kind of premium level should we expect in the future?

For related research, see Martin Weitzman's paper to an NBER seminar in April, A Unified Bayesian Theory of Equity 'Puzzles' ,cited by Brad. While I have not yet given this paper the close reading it deserves, Barro and Weitzmann appear to be making quite similar arguments. Weitzman's paper concludes:

In expositions of the equity premium, risk-free rate, and excess volatility puzzles, the subjective distribution of future growth rates has its mean and variance calibrated to past sample averages. This paper shows that proper Bayesian estimation of uncertain structural growth parameters adds an irreducible fat-tailed background layer of uncertainty that can explain all three puzzles parsimoniously by one unified theory.

Also worth reading, for a different slant on the issue, is the recent Economists' Voice paper by Simon Grant and John Quiggin, What Does the Equity Premium Mean? . The authors argue that taking the equity premium seriously implies that "recessions are extremely costly even if they don’t lower average consumption." John Quiggin writes on his weblog that:

We also show that, to the extent that the equity premium is due to various kinds of capital market failure, it provides a rationale for public ownership of some business enterprises and for a rate of return on public investment close to the real bond rate.

More thoughts on the equity premium puzzle Tyler Cowen, Mark Thoma, Brad DeLong and Washington Monthly's Kevin Drum were among those who picked up my post last week, Has Barro solved the equity premium puzzle? Here's a summary of what they had to say. Tyler Cowen is typically succinct:

If you want my view of the equity premium paradox, we have to ask whether Bryan Caplan is stupid. Choice is context-dependent, and we should not be too worried if no single utility function can account for all of our investment decisions.

Brad DeLong thinks that "Barro has missed something important":

Finance economists talk of the equity premium as a suspiciously low price of stocks relative to the prices of risk-free real bonds. But that's not really correct. In the real world, the equity premium takes the form of a suspiciously low price of stocks relative to short-term nominal government bonds. To say that stock prices relative to nominal bond prices can be explained by the risk of disaster - having a Great Depression or becoming the battleground in a World War - requires that the real value of nominal government bonds not be affected by such a disaster. Yet one standard response of governments to the budget crisis brought on by disaster is inflation.

In order to make Barro's theory work, you need a (1) significant probability of (2) economic disaster that nevertheless (3) does not lead to significant inflation and (4) does not lead to a formal government default. Besides the Great Depression itself, it's hard for me to think of a disaster in the past that fits those four requirements. Typically, inflation means that economic disasters that reduce stock values also reduce real bond values as well: the 1% disaster that removes half your capital stock and cuts real GDP in half also needs to leave the price level and the government's commitment to repaying its bonds unaffected.

Kevin Drum says Barro's answer "is that investors are fundamentally irrational":

[as] they are overestimating the probability of unlikely but catastrophic losses, and this fear makes the demand for risk-free investments larger than it rationally ought to be and thus drives down their price. In other words, the mystery is not so much that returns from stocks are higher than they should be, but that returns from bonds are so low.

...Needless to say, I have nothing to add to this, although it's an explanation I find appealing because of my fondness for Prospect Theory, which is based on the fact that people are not so much risk averse as loss averse. It turns out that most people feel much more strongly about the probability of a loss than they do about the probability of an equivalent gain, and it seems like this is partly what's going on here.

...This debate is far from over, but Barro's contribution is to propose an analytic framework that can be tested. I don't think it can be easily tested, since it relies heavily on perceptions, which are not straightforward things to measure, but at least it's something.

New Canadian blogger Stephen Gordon notes that, as with Martin Weiztman's recent paper, "the main result rests on a returns density with fat tails":

I'm sceptical of these approaches. In the standard expected-utility framework (Arrow, 1971; Lucas, 1978), utility is bounded - as far as I know, no-one has yet extended expected utility analysis to the case where utility is unbounded. The way I see it, the best way to interpret the unbounded utility functions and the densities defined over the entire real line that we use in applied work is that they are convenient approximations to what the theory requires.

But if the approximation is to be a good one, then we need to use distributions such that the model's expected utility over the entire real line is a good approximation for the true expectation over [u0 , u1]. In other words, the contributions of the tails in the calculation of expected utility should be 'small.' Since utility is non-decreasing in consumption, the only way that we can be certain that the tails' contribution will be small is if the density for utility goes to zero fairly quickly outside [u0 , u1]. In this context, it would seem to me that thin-tailed distributions would be preferred to those with fat tails...

Winterspeak provides an account of a buddy who heard Barro present the paper at a University of Chicago seminar:

My take away is that Barro's main point is right - we should consider the possibility of low-probability events. But I still don't think it explains the equity premium. He is still working on his paper - he just discovered Reitz's paper 6 months ago - and right now he uses a very simplistic framework.

One parameter in the framework is the level of risk-aversion in a CRRA framework. Most economists believe a risk-aversion coefficient of about 5 is reasonable, and he finds that with a coefficient of 5 you can explain a lot with a 1% chance per year of an "end of the world" type event for financial markets.

...Well I think that is crazy. I think you might, at most give up $200 in the 60k year to get $100 in the [$30k] bad year--that is a risk-aversion of 1, not 5. So while Barro/Reitz model is good for most economists, it still doesn't explain things to me. Because I think the only reasonable coefficient of risk-aversion based on intuition is about 1, but that predicts virtually no equity premium.

So in conclusion, I think Barro's insight is important and much better than what most economists argue is driving the equity premium. But the equity premium is still a puzzle to me.

[此贴子已经被作者于2005-11-16 20:09:29编辑过]